The Experts below are selected from a list of 5793 Experts worldwide ranked by ideXlab platform
M I Dyachenko - One of the best experts on this subject based on the ideXlab platform.
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smoothness and asymptotic properties of functions with general monotone fourier coefficients
Journal of Fourier Analysis and Applications, 2018Co-Authors: M I Dyachenko, Yu S TikhonovAbstract:In this paper we study Trigonometric Series with general monotone coefficients, i.e., satisfying $$\begin{aligned} \sum \limits _{k=n}^{2n} |a_k - a_{k+1}| \le C \sum \limits _{k=[{n}/{\gamma }]}^{[\gamma n]} \frac{|a_k|}{k}, \quad n\in \mathbb {N}, \end{aligned}$$ for some \(C \ge 1\) and \(\gamma >1\). We first prove the Lebesgue-type inequalities for such Series $$\begin{aligned} n|a_n|\le C \omega (f,1/n). \end{aligned}$$ Moreover, we obtain necessary and sufficient conditions for the sum of such Series to belong to the generalized Lipschitz, Nikolskii, and Zygmund spaces. We also prove similar results for Trigonometric Series with weak monotone coefficients, i.e., satisfying $$\begin{aligned} |a_n | \le C \sum \limits _{k=[{n}/{\gamma }]}^{\infty } \frac{|a_k|}{k}, \quad n\in \mathbb {N}, \end{aligned}$$ for some \(C \ge 1\) and \(\gamma >1\). Sharpness of the obtained results is given. Finally, we study the asymptotic results of Salem–Hardy type.
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uniform convergence of Trigonometric Series with general monotone coefficients
Canadian Journal of Mathematics, 2017Co-Authors: M I Dyachenko, Askhat Mukanov, Sergey TikhonovAbstract:We study criteria for the uniform convergence of Trigonometric Series with general monotone coefficients. We also obtain necessary and sufficient conditions for a given rate of convergence of partial Fourier sums of such Series.
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hardy littlewood theorem for Trigonometric Series with α monotone coefficients
Sbornik Mathematics, 2009Co-Authors: M I Dyachenko, E D NursultanovAbstract:The Hardy-Littlewood theorem is established for Trigonometric Series with α-monotone coefficients. Inequalities of Hardy-Littlewood kind are proved. Examples of Series demonstrating that the results obtained are sharp are constructed. Bibliography: 15 titles.
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the hardy littlewood theorem for Trigonometric Series with generalized monotone coefficients
Russian Mathematics, 2008Co-Authors: M I DyachenkoAbstract:Earlier we introduced a continuous scale of monotony for sequences (classes M α, α ≥ 0), where, for example, M 0 is the set of all nonnegative vanishing sequences, M 1 is the class of all nonincreasing sequences, tending to zero, etc. In addition, we extended several results obtained for Trigonometric Series with monotone convex coefficients onto more general classes. The main result of this paper is a generalization of the well-known Hardy—Littlewood theorem for Trigonometric Series, whose coefficients belong to classes M α, where α ∈ (\( \tfrac{1} {2} \), 1). Namely, the following assertion is true.
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convergence of Trigonometric Series with general monotone coefficients
Comptes Rendus Mathematique, 2007Co-Authors: M I Dyachenko, Sergey TikhonovAbstract:Abstract In this Note we study the convergence results for Trigonometric Series in L p -spaces on one-dimensional and n-dimension torus. The sufficient conditions for these results to hold as well as criteria are written for the Series with general monotone coefficients. The Hardy–Littlewood type theorem is obtained for multiple Series. Several corollaries, in particular, u-convergence are presented. To cite this article: M. Dyachenko, S. Tikhonov, C. R. Acad. Sci. Paris, Ser. I 345 (2007).
Huutai Thai - One of the best experts on this subject based on the ideXlab platform.
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Trigonometric Series solution for analysis of laminated composite beams
Composite Structures, 2017Co-Authors: Trungkien Nguyen, Ngocduong Nguyen, Huutai ThaiAbstract:A new analytical solution based on a higher-order beam theory for static, buckling and vibration of laminated composite beams is proposed in this paper. The governing equations of motion are derived from Lagrange’s equations. An analytical solution based on Trigonometric Series, which satisfies various boundary conditions, is developed to solve the problem. Numerical results are obtained to compare with previous studies and to investigate the effects of length-to-depth ratio, fibre angles and material anisotropy on the deflections, stresses, natural frequencies and critical buckling loads of composite beams with various configurations.
Sergey Tikhonov - One of the best experts on this subject based on the ideXlab platform.
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uniform convergence of Trigonometric Series with general monotone coefficients
Canadian Journal of Mathematics, 2017Co-Authors: M I Dyachenko, Askhat Mukanov, Sergey TikhonovAbstract:We study criteria for the uniform convergence of Trigonometric Series with general monotone coefficients. We also obtain necessary and sufficient conditions for a given rate of convergence of partial Fourier sums of such Series.
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best approximation and moduli of smoothness computation and equivalence theorems
Journal of Approximation Theory, 2008Co-Authors: Sergey TikhonovAbstract:In this paper we investigate the Trigonometric Series with the @b-general monotone coefficients. First, we study the uniform convergence criterion. The estimates of best approximations and moduli of smoothness of the Series in uniform metrics are obtained in terms of coefficients. These results imply several important relations between moduli of smoothness of different orders (in particular, Marchaud-type inequality) and best approximations.
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convergence of Trigonometric Series with general monotone coefficients
Comptes Rendus Mathematique, 2007Co-Authors: M I Dyachenko, Sergey TikhonovAbstract:Abstract In this Note we study the convergence results for Trigonometric Series in L p -spaces on one-dimensional and n-dimension torus. The sufficient conditions for these results to hold as well as criteria are written for the Series with general monotone coefficients. The Hardy–Littlewood type theorem is obtained for multiple Series. Several corollaries, in particular, u-convergence are presented. To cite this article: M. Dyachenko, S. Tikhonov, C. R. Acad. Sci. Paris, Ser. I 345 (2007).
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Trigonometric Series with general monotone coefficients
Journal of Mathematical Analysis and Applications, 2007Co-Authors: Sergey TikhonovAbstract:We study Trigonometric Series with general monotone coefficients. Convergence results in the different metrics are obtained. Also, we prove a Hardy-type result on the behavior of the Series near the origin.
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Trigonometric Series of nikol skii classes
Acta Mathematica Hungarica, 2007Co-Authors: Sergey TikhonovAbstract:We study when sums of Trigonometric Series belong to given function classes. For this purpose we describe the Nikol’skii class of functions and, in particular, the generalized Lipschitz class. Results for Series with positive and general monotone coefficients are presented.
Trungkien Nguyen - One of the best experts on this subject based on the ideXlab platform.
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Trigonometric Series solution for analysis of laminated composite beams
Composite Structures, 2017Co-Authors: Trungkien Nguyen, Ngocduong Nguyen, Huutai ThaiAbstract:A new analytical solution based on a higher-order beam theory for static, buckling and vibration of laminated composite beams is proposed in this paper. The governing equations of motion are derived from Lagrange’s equations. An analytical solution based on Trigonometric Series, which satisfies various boundary conditions, is developed to solve the problem. Numerical results are obtained to compare with previous studies and to investigate the effects of length-to-depth ratio, fibre angles and material anisotropy on the deflections, stresses, natural frequencies and critical buckling loads of composite beams with various configurations.
Ngocduong Nguyen - One of the best experts on this subject based on the ideXlab platform.
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Trigonometric Series solution for analysis of laminated composite beams
Composite Structures, 2017Co-Authors: Trungkien Nguyen, Ngocduong Nguyen, Huutai ThaiAbstract:A new analytical solution based on a higher-order beam theory for static, buckling and vibration of laminated composite beams is proposed in this paper. The governing equations of motion are derived from Lagrange’s equations. An analytical solution based on Trigonometric Series, which satisfies various boundary conditions, is developed to solve the problem. Numerical results are obtained to compare with previous studies and to investigate the effects of length-to-depth ratio, fibre angles and material anisotropy on the deflections, stresses, natural frequencies and critical buckling loads of composite beams with various configurations.
